Asked by Piwo
Prove:
1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA
1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA
Answers
Answered by
Rikkard
1/cos^2A -sin^2A + 2cosAsinA/cos^2A -sin^2A = 1+2cosAsinA/cos^2A -sin^2A
I used the trig identies to expand 1/cos2A and sin2A/cos2A and added the together because they have the same denominator.
How I got from 1 to cos^2+sin^2 is by trig identity cos^2+sin^2=1.
1+2cosAsinA/cos^2A -sin^2A ==> cos^2+sin^2+2cosAsinA/cos^2A -sin^2A (factorise this equation both the numerator and denominator which will give you the following: )
(cosA+sinA)(cosA+sinA)/(cosA+sinA)(cosA-sinA) (Cancel out the common factors)
cosA+sinA/cosA-sinA
Hope this makes sense!
I used the trig identies to expand 1/cos2A and sin2A/cos2A and added the together because they have the same denominator.
How I got from 1 to cos^2+sin^2 is by trig identity cos^2+sin^2=1.
1+2cosAsinA/cos^2A -sin^2A ==> cos^2+sin^2+2cosAsinA/cos^2A -sin^2A (factorise this equation both the numerator and denominator which will give you the following: )
(cosA+sinA)(cosA+sinA)/(cosA+sinA)(cosA-sinA) (Cancel out the common factors)
cosA+sinA/cosA-sinA
Hope this makes sense!
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